“I hope I would notice my own severe confusion and then assign >50% probability to the majority vote.”
On a group level, I wouldn’t think it’s a particularly rational path to mimic the majority, even if you believe that they’re honestly reporting. If you had a group of, say, 10 people, and the first 5 all gave the wrong answer, there would then be a rational impetuous for everyone subsequent to mimic that wrong answer on the logic that “the last (5-9) people all said C, so clearly p(C) > 0.5”.
Far better to dissent and provide the group with new information.
Ooh, that’s really interesting. The best solution might actually be to say the full statement, “I see B as equal, but since the other 5 people before me said C, C is probably objectively more likely.” Then future people after you can still hear what you saw, independently of what you inferred based on others.
But I think there are a lot of other really interesting problems embedded in this, involving the feedback between semi-Bayesians trying to use each other to process evidence. (True Bayesians get the right answer; but what answer to semi-Bayesians get?)
On a group level, I wouldn’t think it’s a particularly rational path to mimic the majority, even if you believe that they’re honestly reporting. If you had a group of, say, 10 people, and the first 5 all gave the wrong answer, there would then be a rational impetuous for everyone subsequent to mimic that wrong answer on the logic that “the last (5-9) people all said C, so clearly p(C) > 0.5”.
Far better to dissent and provide the group with new information.
Ooh, that’s really interesting. The best solution might actually be to say the full statement, “I see B as equal, but since the other 5 people before me said C, C is probably objectively more likely.” Then future people after you can still hear what you saw, independently of what you inferred based on others.
But I think there are a lot of other really interesting problems embedded in this, involving the feedback between semi-Bayesians trying to use each other to process evidence. (True Bayesians get the right answer; but what answer to semi-Bayesians get?)